Relative to a fixed origin OOO, the point D D\,D has position vector (−2i+4j+k)(-2\mathbf{i} + 4\mathbf{j} + \mathbf{k})(−2i+4j+k), the point E E\,E has position vector (−3i+6j−3k)(-3\mathbf{i} + 6\mathbf{j} - 3\mathbf{k})(−3i+6j−3k), and the point F F\,F has position vector (4i−8j+16k)(4\mathbf{i} - 8\mathbf{j} + 16\mathbf{k})(4i−8j+16k).
Find DE⃗\vec{DE}DE
Show that the quadrilateral ODEF ODEF\,ODEF is a trapezium, giving reasons for your answer.
109 exam-style questions on Edexcel A Level Maths Vectors, covering 12.1 3D Coordinates, 12.2 Vectors in 3D, 12.3 Solving Geometric Problems, and 12.4 Application to Mechanics. Each one has a worked solution and a mark scheme showing where the marks go.